2. (10 points) Suppose that (Y), are iid random variables such that P(Y; = 1) =p and P(Y; = -1)=1-p. Define the process (X) by the following recursive relationship Xo = 0 and if X-1+ Yn <-2 -2 Xn Xn-1+Yn if-2 X-1+ Yn <2 2 if Xn-1+Yn>2 for n 1 integers. (a) Clearly justify that (X) is a stationary discrete time Markov chain, (b) Find its state space S (c) Calculate its transition matrix P (making sure the entries in P are ordered consistently with the ordering you gave for S).